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        <title>API docs for &ldquo;sympy.geometry.ellipse.Ellipse&rdquo;</title>
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        <body><h1 class="class">Class s.g.e.Ellipse(<a href="sympy.geometry.entity.GeometryEntity.html">GeometryEntity</a>):</h1><span id="part">Part of <a href="sympy.geometry.ellipse.html">sympy.geometry.ellipse</a></span><p>known subclasses: <a href="sympy.geometry.ellipse.Circle.html">sympy.geometry.ellipse.Circle</a></p><div class="toplevel"><div><p>An ellipse in space. Constructed from a center and two radii, the first 
being the horizontal radius (along the x-axis) and the second being the 
vertical radius (along the y-axis).</p>
<h1 class="heading">Notes:</h1>
  <ul>
    <li>
      Rotation is currently not supported since an ellipse is defined on 
      horizontal/vertical radii
    </li>
  </ul>
<h1 class="heading">Example:</h1>
<pre class="py-doctest">
<span class="py-prompt">&gt;&gt;&gt; </span>e = Ellipse(Point(0, 0), 5, 1)
<span class="py-prompt">&gt;&gt;&gt; </span>e.hradius, e.vradius
<span class="py-output">(5, 1)</span></pre>
  <h2 class="heading">Plotting example</h2>
    <p>In [1]: c1 = Circle(Point(0,0), 1)</p>
    <p>In [2]: Plot(c1) Out[2]: [0]: cos(t), sin(t), 'mode=parametric'</p>
    <p>In [3]: p = Plot()</p>
    <p>In [4]: p[0] = c1</p>
    <p>In [5]: radius = Segment(c1.center, c1.random_point())</p>
    <p>In [6]: p[1] = radius</p>
    <p>In [7]: p Out[7]: [0]: cos(t), sin(t), 'mode=parametric' [1]: 
    t*cos(1.546086215036205357975518382), 
    t*sin(1.546086215036205357975518382), 'mode=parametric'</p>
</div></div><table class="children"><tr class="function"><td>Function</td><td><a href="#sympy.geometry.ellipse.Ellipse.__new__">__new__</a></td><td><span class="undocumented">Undocumented</span></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.geometry.ellipse.Ellipse.center">center</a></td><td><div><p>The center of the ellipse.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.geometry.ellipse.Ellipse.hradius">hradius</a></td><td><div><p>The horizontal radius of the ellipse.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.geometry.ellipse.Ellipse.vradius">vradius</a></td><td><div><p>The vertical radius of the ellipse.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.geometry.ellipse.Ellipse.area">area</a></td><td><div><p>The area of the ellipse.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.geometry.ellipse.Ellipse.circumference">circumference</a></td><td><div><p>The circumference of the ellipse.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.geometry.ellipse.Ellipse.foci">foci</a></td><td><div><p>The foci of the ellipse, if the radii are numerical.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.geometry.ellipse.Ellipse.tangent_line">tangent_line</a></td><td><div><p>If p is on the ellipse, returns the tangent line through point p.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.geometry.ellipse.Ellipse.is_tangent">is_tangent</a></td><td><div><p>Returns True if o is tangent to the ellipse, False otherwise.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.geometry.ellipse.Ellipse.arbitrary_point">arbitrary_point</a></td><td><div><p>Returns a symbolic point that is on the ellipse.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.geometry.ellipse.Ellipse.plot_interval">plot_interval</a></td><td><div><p>Returns a typical plot interval used by the plotting module.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.geometry.ellipse.Ellipse.random_point">random_point</a></td><td><div><p>Returns a random point on the ellipse.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.geometry.ellipse.Ellipse.equation">equation</a></td><td><div><p>Returns the equation of the ellipse.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.geometry.ellipse.Ellipse._do_line_intersection">_do_line_intersection</a></td><td><div><p>Find the intersection of a LinearEntity and the ellipse. Makes no</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.geometry.ellipse.Ellipse.intersection">intersection</a></td><td><div><p>Returns a list of all of the intersections of this entity and 
another</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.geometry.ellipse.Ellipse.__eq__">__eq__</a></td><td><span class="undocumented">Undocumented</span></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.geometry.ellipse.Ellipse.__contains__">__contains__</a></td><td><span class="undocumented">Undocumented</span></td></tr></table>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.geometry.ellipse.Ellipse.__new__">__new__(cls, center, hradius, vradius, **kwargs):</a></div>
            <div class="functionBody"><div class="undocumented">Undocumented</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.geometry.ellipse.Ellipse.center">center(self):</a></div>
            <div class="functionBody"><div><p>The center of the ellipse.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.geometry.ellipse.Ellipse.hradius">hradius(self):</a></div>
            <div class="functionBody"><div><p>The horizontal radius of the ellipse.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.geometry.ellipse.Ellipse.vradius">vradius(self):</a></div>
            <div class="functionBody"><div><p>The vertical radius of the ellipse.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.geometry.ellipse.Ellipse.area">area(self):</a></div>
            <div class="functionBody"><div><p>The area of the ellipse.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.geometry.ellipse.Ellipse.circumference">circumference(self):</a></div>
            <div class="functionBody"><div><p>The circumference of the ellipse.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.geometry.ellipse.Ellipse.foci">foci(self):</a></div>
            <div class="functionBody"><div><p>The foci of the ellipse, if the radii are numerical.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.geometry.ellipse.Ellipse.tangent_line">tangent_line(self, p):</a></div>
            <div class="functionBody"><div><p>If p is on the ellipse, returns the tangent line through point p. 
Otherwise, returns the tangent line(s) from p to the ellipse, or None if no
tangent line is possible (e.g., p inside ellipse).</p>
<p>Example:</p>
<p>In [1]: e = Ellipse(Point(0,0), 3, 2)</p>
<p>In [2]: t = e.tangent_line(e.random_point())</p>
<p>In [3]: p = Plot()</p>
<p>In [4]: p[0] = e</p>
<p>In [5]: p[1] = t</p>
<p>The above will plot an ellipse together with a tangent line.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.geometry.ellipse.Ellipse.is_tangent">is_tangent(self, o):</a></div>
            <div class="functionBody"><div><p>Returns True if o is tangent to the ellipse, False otherwise.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.geometry.ellipse.Ellipse.arbitrary_point">arbitrary_point(self, parameter_name='t'):</a></div>
            <div class="functionBody"><div><p>Returns a symbolic point that is on the ellipse.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.geometry.ellipse.Ellipse.plot_interval">plot_interval(self, parameter_name='t'):</a></div>
            <div class="functionBody"><div><p>Returns a typical plot interval used by the plotting module.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.geometry.ellipse.Ellipse.random_point">random_point(self):</a></div>
            <div class="functionBody"><div><p>Returns a random point on the ellipse.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.geometry.ellipse.Ellipse.equation">equation(self, x='x', y='y'):</a></div>
            <div class="functionBody"><div><p>Returns the equation of the ellipse.</p>
<p>Optional parameters x and y can be used to specify symbols, or the names
of the symbols used in the equation.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.geometry.ellipse.Ellipse._do_line_intersection">_do_line_intersection(self, o):</a></div>
            <div class="functionBody"><div><p>Find the intersection of a LinearEntity and the ellipse. Makes no 
regards to what the LinearEntity is because it assumes a Line. To ensure 
correct intersection results one must invoke intersection() to remove bad 
results.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.geometry.ellipse.Ellipse.intersection">intersection(self, o):</a></div>
            <div class="functionBody"><div><p>Returns a list of all of the intersections of this entity and another 
entity.</p>
<h1 class="heading">Notes:</h1>
  <ul>
    <li>
      This method is not intended to be used directly but rather through 
      the intersection() method found in util.py.
    </li>
    <li>
      An entity is not required to implement this method.
    </li>
    <li>
      If two different types of entities can intersect, it is only required
      that one of them be able to determine this.
    </li>
  </ul>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.geometry.ellipse.Ellipse.__eq__">__eq__(self, o):</a></div>
            <div class="functionBody"><div class="undocumented">Undocumented</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.geometry.ellipse.Ellipse.__contains__">__contains__(self, o):</a></div>
            <div class="functionBody"><div class="undocumented">Undocumented</div></div>
            </div></body>
        